Put on a heavy pair of gloves. Cut a segment from a healthy section of the cactus with a clean knife. Slice through a joint between two segments. For barrel-type cacti, cut a small barrel that is forming on a larger barrel or growing next to the larger barrel.
Lay the cutting on a paper plate in a shaded area. Allow the cut edge to dry, or scab over and dry, which can take between 24 hours and several days depending on the thickness of the cutting.
Fill a 6-inch-diameter pot with equal parts peat moss and perlite, thoroughly mixed together. Water the potting mix until it is barely moistened throughout. Use pots that contain a bottom drainage hole so the soil doesn't retain too much moisture.
Push the bottom half of the cactus segment into the potting mix so the segment stands upright on its own. Set the pot in a 60-degree Fahrenheit or warmer location to root.
Water the cutting when the soil begins to dry out and is barely damp. Provide just enough water to moisten the soil and empty any drained water promptly from the drip tray beneath the pot.